Same even but two different probabilites
$begingroup$
I'm having problem wrapping my head around the following scenario:
Suppose there's a gory murder in the island of Onewaynia. Two persons have been shortlisted (and it's guaranteed by divine forces that one and only one of them is the murderer), Mr X and Mr Y. The common people don't know who are shortlisted however (they don't know the identity of X/Y), however the commissioner do.
Morever, suppose that there's traces of blood AB near the murder scene and it's guranteed the murderer has blood AB. Among the general population, 1 % (i.e with probability 0.01) people has blood AB.
Person X is tested to have blood AB. The blood group of Y is not tested. What's the probability that Y has blood group AB, if you (a) Ask the commissioner (b) Ask a common man ?
I am having very confusions with this problem. Isn't the probability of Y having blood group AB is 0.01 regardless of who you ask ?
But the book is telling that the commissioner would tell that Y has a higher chance of having blood group AB because Y has 50% chance of being the murderer. But can't the commissioner just ignore the information that Y is shortlisted the murderer and churn of the answer of p = 0.01 ?
Why should the truth value depend on the person you're asking ? Why having the knowledge that Y is shortlisted (but not knowing any other thing about Y) increases the probability ?
probability conditional-expectation conditional-probability bayesian bayes-theorem
asked Jan 2 at 12:26
alxchenalxchen
604421
$endgroup$
add a comment |
$begingroup$
I'm having problem wrapping my head around the following scenario:
Suppose there's a gory murder in the island of Onewaynia. Two persons have been shortlisted (and it's guaranteed by divine forces that one and only one of them is the murderer), Mr X and Mr Y. The common people don't know who are shortlisted however (they don't know the identity of X/Y), however the commissioner do.
Morever, suppose that there's traces of blood AB near the murder scene and it's guranteed the murderer has blood AB. Among the general population, 1 % (i.e with probability 0.01) people has blood AB.
Person X is tested to have blood AB. The blood group of Y is not tested. What's the probability that Y has blood group AB, if you (a) Ask the commissioner (b) Ask a common man ?
I am having very confusions with this problem. Isn't the probability of Y having blood group AB is 0.01 regardless of who you ask ?
But the book is telling that the commissioner would tell that Y has a higher chance of having blood group AB because Y has 50% chance of being the murderer. But can't the commissioner just ignore the information that Y is shortlisted the murderer and churn of the answer of p = 0.01 ?
Why should the truth value depend on the person you're asking ? Why having the knowledge that Y is shortlisted (but not knowing any other thing about Y) increases the probability ?
probability conditional-expectation conditional-probability bayesian bayes-theorem
asked Jan 2 at 12:26
alxchenalxchen
604421
$endgroup$
$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
1
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36
add a comment |
$begingroup$
I'm having problem wrapping my head around the following scenario:
Suppose there's a gory murder in the island of Onewaynia. Two persons have been shortlisted (and it's guaranteed by divine forces that one and only one of them is the murderer), Mr X and Mr Y. The common people don't know who are shortlisted however (they don't know the identity of X/Y), however the commissioner do.
Morever, suppose that there's traces of blood AB near the murder scene and it's guranteed the murderer has blood AB. Among the general population, 1 % (i.e with probability 0.01) people has blood AB.
Person X is tested to have blood AB. The blood group of Y is not tested. What's the probability that Y has blood group AB, if you (a) Ask the commissioner (b) Ask a common man ?
I am having very confusions with this problem. Isn't the probability of Y having blood group AB is 0.01 regardless of who you ask ?
But the book is telling that the commissioner would tell that Y has a higher chance of having blood group AB because Y has 50% chance of being the murderer. But can't the commissioner just ignore the information that Y is shortlisted the murderer and churn of the answer of p = 0.01 ?
Why should the truth value depend on the person you're asking ? Why having the knowledge that Y is shortlisted (but not knowing any other thing about Y) increases the probability ?
probability conditional-expectation conditional-probability bayesian bayes-theorem
asked Jan 2 at 12:26
alxchenalxchen
604421
$endgroup$
I'm having problem wrapping my head around the following scenario:
Suppose there's a gory murder in the island of Onewaynia. Two persons have been shortlisted (and it's guaranteed by divine forces that one and only one of them is the murderer), Mr X and Mr Y. The common people don't know who are shortlisted however (they don't know the identity of X/Y), however the commissioner do.
Morever, suppose that there's traces of blood AB near the murder scene and it's guranteed the murderer has blood AB. Among the general population, 1 % (i.e with probability 0.01) people has blood AB.
Person X is tested to have blood AB. The blood group of Y is not tested. What's the probability that Y has blood group AB, if you (a) Ask the commissioner (b) Ask a common man ?
I am having very confusions with this problem. Isn't the probability of Y having blood group AB is 0.01 regardless of who you ask ?
But the book is telling that the commissioner would tell that Y has a higher chance of having blood group AB because Y has 50% chance of being the murderer. But can't the commissioner just ignore the information that Y is shortlisted the murderer and churn of the answer of p = 0.01 ?
Why should the truth value depend on the person you're asking ? Why having the knowledge that Y is shortlisted (but not knowing any other thing about Y) increases the probability ?
probability conditional-expectation conditional-probability bayesian bayes-theorem
probability conditional-expectation conditional-probability bayesian bayes-theorem
asked Jan 2 at 12:26
alxchenalxchen
604421
asked Jan 2 at 12:26
alxchenalxchen
604421
asked Jan 2 at 12:26
alxchenalxchen
604421
asked Jan 2 at 12:26
alxchenalxchen
604421
asked Jan 2 at 12:26
alxchenalxchen
604421
604421
$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
1
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36
add a comment |
$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
1
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36
$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
1
1
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36
add a comment |
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$begingroup$
The fact that $Y$ has a priori $.5$ probability of having committed the murder changes your estimate for $Y's$ probability of having $AB$ blood. As you get more information about a situation your estimate for the relevant probabilities changes.
$endgroup$
– lulu
Jan 2 at 12:29
$begingroup$
@lulu But why should that change the probability ? Can't I just ignore the fact I know that Y has a priori .5 probability of being the murderer ?
$endgroup$
– alxchen
Jan 2 at 12:30
$begingroup$
Of course if you ignore information then you get a different probability, but the problem is asking for your estimate of the probability assuming you use all the information you are given.
$endgroup$
– lulu
Jan 2 at 12:32
1
$begingroup$
Suppose I know that, in general, there is a $10%$ chance of rain. Now I look around around me and see that everyone coming in from the outside is either soaking wet or is carrying an umbrella. At this point, my estimate of the probability has gone way up (to near $100%$). Why would I ignore all the information I possess?
$endgroup$
– lulu
Jan 2 at 12:35
$begingroup$
@lulu Thanks and that makes sense ! Nice example :)
$endgroup$
– alxchen
Jan 2 at 12:36